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A329631 Irregular triangle read by rows where row n lists the prime indices of the n-th squarefree number.

%I A329631 #5 Nov 19 2019 16:36:13
%S A329631 1,2,3,1,2,4,1,3,5,6,1,4,2,3,7,8,2,4,1,5,9,1,6,10,1,2,3,11,2,5,1,7,3,
%T A329631 4,12,1,8,2,6,13,1,2,4,14,1,9,15,2,7,16,3,5,2,8,1,10,17,18,1,11,3,6,1,
%U A329631 2,5,19,2,9,1,3,4,20,21,1,12,4,5,1,2,6
%N A329631 Irregular triangle read by rows where row n lists the prime indices of the n-th squarefree number.
%C A329631 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e A329631 Triangle begins:
%e A329631    1: {}         33: {2,5}      66: {1,2,5}     97: {25}
%e A329631    2: {1}        34: {1,7}      67: {19}       101: {26}
%e A329631    3: {2}        35: {3,4}      69: {2,9}      102: {1,2,7}
%e A329631    5: {3}        37: {12}       70: {1,3,4}    103: {27}
%e A329631    6: {1,2}      38: {1,8}      71: {20}       105: {2,3,4}
%e A329631    7: {4}        39: {2,6}      73: {21}       106: {1,16}
%e A329631   10: {1,3}      41: {13}       74: {1,12}     107: {28}
%e A329631   11: {5}        42: {1,2,4}    77: {4,5}      109: {29}
%e A329631   13: {6}        43: {14}       78: {1,2,6}    110: {1,3,5}
%e A329631   14: {1,4}      46: {1,9}      79: {22}       111: {2,12}
%e A329631   15: {2,3}      47: {15}       82: {1,13}     113: {30}
%e A329631   17: {7}        51: {2,7}      83: {23}       114: {1,2,8}
%e A329631   19: {8}        53: {16}       85: {3,7}      115: {3,9}
%e A329631   21: {2,4}      55: {3,5}      86: {1,14}     118: {1,17}
%e A329631   22: {1,5}      57: {2,8}      87: {2,10}     119: {4,7}
%e A329631   23: {9}        58: {1,10}     89: {24}       122: {1,18}
%e A329631   26: {1,6}      59: {17}       91: {4,6}      123: {2,13}
%e A329631   29: {10}       61: {18}       93: {2,11}     127: {31}
%e A329631   30: {1,2,3}    62: {1,11}     94: {1,15}     129: {2,14}
%e A329631   31: {11}       65: {3,6}      95: {3,8}      130: {1,3,6}
%t A329631 Table[PrimePi/@First/@If[k==1,{},FactorInteger[k]],{k,Select[Range[30],SquareFreeQ]}]
%Y A329631 Row sums are A319246.
%Y A329631 Row lengths are A072047.
%Y A329631 Same as A319247 with rows reversed.
%Y A329631 Composition of A000720 and A265668.
%Y A329631 Looking at all numbers instead of just squarefree numbers gives A112798.
%Y A329631 Cf. A000009, A005117, A048672, A056239, A299755, A302590.
%K A329631 nonn,tabf
%O A329631 1,2
%A A329631 _Gus Wiseman_, Nov 18 2019